This invention relates to an active retrodirective array (ARA) antenna, and more particularly to a phase conjugation circuit which eliminates squint in a large ARA.
Systems employing retrodirective antennas receive and transmit (retrodirect) signals at different frequencies in order to provide input-output isolation. Such retrodirective antenna systems have been disclosed in repeaters for satellite communications systems. Representative of this prior art are patents to Margerum U.S. Pat. Nos. (3,300,782), Stahler (3,350,642), Preikschat et al (3,611,381), Raabe (3,757,334) and Albert (3,898,663). The problem with this prior art is that the phase conjugation circuits are not "exact" resulting in a pointing error known as "squint." The term "exact" as applied to phase conjugation is defined below.
In some applications it is necessary to retrodirect a narrow beam from a large antenna array on a satellite, and to continually steer the retrodirected beam to the center of a receiving antenna on the ground. Though not yet in practical use, ARA's are expected to become an important part of phased array technology. They have been proposed for such applications as satellite communication networks, aircraft transponders, and even for microwave powder transmission from an orbiting solar power station. The ARA steers a beam towards the apparent source of an illuminating signal called the pilot signal. In the case of communication satellites, for example, the pilot signal would be transmitted from a ground station with which the satellite communicates.
Much of the current interest in ARA's is centered about its possible application to a solar power satellite (SPS). The SPS would be placed in a geosynchronous orbit. Several gigawatts of microwave power, generated by and converted from the dc output of huge solar cell panels, would be transmitted to a rectifying antenna ("rectenna") on the Earth's surface. The SPS-rectenna range would be 36,000 km, the rectenna diameter 7.4 km, and the frequency S-band (.lambda..apprxeq.12.5 cm). These parameters plus stringent sidelobe requirements imply a transmitting antenna on the SPS about 1.0 km in diameter. The pointing loss becomes unacceptable if the miss radius exceeds 200 m, which, in angular terms, corresponds to 5.6.times.10.sup.-6 radians=1.1 arc seconds. Because of the obvious difficulty in mechanically pointing a 1.0 km diameter antenna to this accuracy, the proponent of the SPS suggest using an ARA for the spacecraft antenna with the pilot source located at the center of the rectenna.
An equally important reason for using an ARA for the SPS is safety, specifically, the need to protect the public from exposure to the high power beam. Although no beam pointing system is infallible, the ARA would seem to be the most inherently reliable system for this application since its retrodirectivity is inseparable from the beam forming process itself. Such pointing errors that are known to exist produce only slight (compared to rectenna diameter) mispointing. Moreover, the response time of an ARA is determined by its own dimensions, not by the ground to spacecraft round trip delay as it would be for a conventional closed loop control system. It would, therefore, be of the order of microseconds, not 2.times.36.times.10.sup.6 /(3.times.10.sup.8)=0.24 seconds, the round trip delay for an SPS in geosynchronous orbit.
The applicability of ARA's to communication satellites has also been noted. Large antennas on communication satellites will be required not only to serve ground receivers with small apertures (as in direct TV transmissions), but also to provide the directivity needed for spectrum conservation. A communication satellite ARA could use either frequency or time division multiplexing. In a frequency multiplexed version designed to communicate with each of N ground station, each element of the array is equipped with N phase conjugation circuits, and each circuit responds only to the carrier frequency of the pilot signal transmitted by one of the N stations. Information modulated on the carrier of the pilot signal from one of the stations, call it Station A, is demodulated and remodulated onto the carriers of downlink signals retrodirected to one or more of the other ground stations. Similarly, information from any of these other stations can be simultaneously modulated onto the downlink to A. The average power available for each downlink must, of course, decrease with N, but the full gain of the array is available to each downlink independently of N.
If time division instead of frequency multiplexing is used, only one phase conjugation circuit and one receiver is required for each element. However, the bandwidth of that receiver must be N times greater than that of each of the N receivers required in the frequency multiplex case. Depending on the dimensions of the array, the required bandwidth, and the scan angles required to point beams at different ground stations, time delay compensation may be required in order to properly synchronize the data streams transmitted by the various elements.
ARA's may also be useful as deep space probe antennas. As the distance times data rate product increases, it will eventually become necessary to use spacecraft apertures too large to be mechanically pointed. Here, however, certain errors proportional to the velocity of the spacecraft relative to the ground station may become important. They are unimportant in geosynchronous satellites, such as the SPS and most communication satellites, because of their small relative velocities, but deep space probes may experience much higher velocities in the course of a mission, and this factor may limit the size of the ARA which can be used on such spacecraft.
It has been noted above that an ARA can function as a receiving array. Such arrays may be useful for receiving weak signals from very distant deep space probes or as radio astronomy arrays. Since low noise front ends are fairly expensive, such an array would probably consist of a modest number of fairly large antennas rather than a very large number of small elements. Each of the large elements would be mechanically steered to keep the source within its beamwidth. As in communication satellite ARA's, data processing may be required to remove time delay distortion.
An improved method and apparatus for an active retrodirective antenna which uses "central phasing" is disclosed in a copending application Ser. No. 777,983 filed Mar. 16, 1977. Before briefly summarizing the concept of "central phasing," a definition of terms and important principles will first be introduced.
An active retrodirective array (ARA) transmits a beam towards the apparent source of an illuminating signalcalled the pilot. "Active" implies that the array produces, not merely reflects, RF power. Retrodirectivity is achieved by retransmitting from each element of the array a signal whose phase is the "conjugate" of that received by the element. Assuming that the phase of the pilot signal of angular frequency .omega. received by the kth element of the array at time t is EQU .phi..sub.k (t)=.omega.(t-r.sub.k /c) (1)
where r.sub.k is the distance from the kth element to the source of the pilot signal, we define the conjugate of .phi..sub.k to be EQU .phi..sub.k * (t)=.omega.'(t+r.sub.k /c)+.theta..sub.o ( 2)
where .omega.' is the angular frequency of the conjugate signal, which in general is not the same as that of the pilot signal, and .theta..sub.o is an arbitrary phase offset which must, however, be constant over the entire array. In order to do this, each element of the array must be equipped with a phase conjugation circuit (PCC). The phase of the signal received from the kth element by a receiver located at the pilot source (4=o) is, at time t, EQU .phi..sub.k * (t,o)=.omega.'(t+r.sub.k /c-r.sub.k /c)+.theta..sub.o =.omega.'t+.theta..sub.o ( 3)
Thus the contributions to the field at r=o from the various elements of the array are all in phase at that point, which means that the beam points toward the pilot source.
Previous definitions of phase conjugation included only the case .omega.'=.omega.. Here the definition is generalized in order to emphasize that .omega.'=.omega. is neither necessary nor desirable; retrodirectivity holds in either case provided only that the propagation medium is non-dispersive, and .omega.'=.omega. is usually to be avoided because of input-output isolation problems.
The term "exact conjugation" means that Equation (2) is satisifed exactly, rather than approximately. In a planar array (the most common geometry for antenna arrays) the effect of inexact conjugation is to misdirect (squint) the beam by an angle proportional to both the scan angle (the angle of incidence of the pilot signal) and the ratio .omega.'/.omega.. Thus, in applications requiring very precise beam pointing, phase conjugation for each array element must be exact to avoid squint. It is also evident that the phase conjugation circuit (PCC) design must avoid any "mixer degeneracy" which may cause large unpredictable phase errors. Prior art phase conjugators which shift the received signal frequency in generating a conjugate signal do so in a manner which results in inexact phase conjugation.
"Mixer degeneracy" refers to either of two cases: a down-converter in which the frequency of one of the inputs is twice that of the other, or an up-converter with equal input frequencies. In either case the output signal contains two components with distinct phases. Only one of these components has, in general, the correct phase, but due to their common frequency, the two components are indistinguishable. Hence a phase error is produced of a magnitude that depends upon the vector sum of the two components.
An ARA can also function as a receiving (i.e., tracking) array. It is easy to show how a single PCC at each element can be used for both functions, receiving as well as transmitting, simultaneously, with little additional equipment.
From Equations (1) and (2) it is seen that phase conjugation amounts to advancing the phase of an input signal by an amount equal to its delay. The phase conjugation circuit (PCC) must, therefore, be provided with a phase reference against which to measure that delay. If each PCC is located at its associated ARA element, then it is clear that the phase reference must be transmitted to each PCC from some central source via transmission lines of equal phase delay modulo 2.pi.. But it may be difficult to do this if the transmission lines are very long. For example, consider the 1.0 km diameter SPS ARA described above operating at S-band (.lambda.=12.5 cm). If the master phase reference is located at the center of the disk, the transmission lines to elements at the periphery will be 500 m long. In order to keep the phase delay in this line constant to within .pi./10 radians, its length must not vary by more than .+-..lambda./20 cm, or a relative change no greater than .+-.1.2.times.10.sup. -5. But this length change would be produced in an aluminum line by a temperature change of only 0.5 degrees C, or by a mechanical stress of only 120 psi. The results for other good conductors are similar. Since it is reasonable to expect temperature and stress changes far greater than these in this huge structure, it is clear that the required dimensional stability cannot be met with materials commonly used for transmission lines.
While it might be possible to solve this problem with uncommon materials, it is possible to avoid it altogether by locating all PCC's at the reference source rather than at their respective elements. This method of providing the phase reference is referred to above as "central phasing" and will be described more fully hereinafter. The phase reference for this ARA is the pilot signal received by the 0-th, or reference, element. The pilot signal received by the kth element is transmitted to its associated PCC located at the reference element via a transmission line and diplexer. The PCC conjugates the entire phase delay, i.e. the sum of the space delay, .omega.r.sub.k /c, and the transmission line delay, .omega.l.sub.ko /c.sub.L, where c.sub.L is the phase velocity of the line, and transmits that conjugate signal back down the same transmission line to the kth element, which retransmits it. Its phase at that point is .omega.'(t+r.sub.k /c)+.theta..sub.o which is exactly what it would be were the PCC located at the kth element rather than at the reference element. Thus the length of the transmission line is immaterial provided only that: first the line is dispersionless, and second its length is constant with time.
The importance of central phasing lies in the fact that it liberates the ARA from the rigid structure which would otherwise be needed in order to realize accurate retrodirectivity. The elements need not be arranged in any particular geometrical pattern, and may, in fact, move about with respect to one another provided the movement is not too rapid. This applies, of course, only to pointing accuracy, not to side lobe levels or other characteristics of the antenna array.
Locating all the PCC's in one small volume very near the reference element may be difficult if the array contains thousands of elements. A modification of the central phasing concept using a tree topology (in which the phase reference is regenerated at each node and which will be required in such large arrays) is disclosed in the aforesaid application. Each branch of the tree consists of a PCC, located near the node, and an element of the ARA at the end of a transmission line. A phase reference supplies all the PCC's connected to a node. At the initial node, this is the reference element of the array. At subsequent nodes, it is a phase reference regenerator (PRR). The PRR combines samples of the pilot and conjugate signals at an element to reproduce the original reference. Since the signal paths within these nodes assemblies are unilateral, their phase delays must be carefully balanced in order to avoid phase error buildup at successive nodes. In order to assure the stability of the phase delay balance, these assemblies must be uniform and compact. Critical applications may require temperature stabilization of some active elements.
The number of nodes in a tree is relatively small even for an ARA of several thousand elements. For example, with six branches at each node, a tree of only five nodes suffices for an array of 9331 elements. PRRs are required only at the first through fourth order nodes of this tree. A PRR at a fourth order node is the last in a chain of four PRRs connecting the PCCs at that fourth order node to the reference elements of the ARA. The error in the value of the phase reference produced by this last PRR is the sum of the errors arising in all the PRR's in the chain. If these errors arise from independent and identical random processes in each PRR, then the probable error of the output of the last PRR is .sqroot.4 (PE).sup.2 =2 (PE) where PE is the probable error of each PRR. Thus the error buildup due to repeated regeneration of the phase reference is moderate even for large arrays.